∵AB∥CD,
∴∠BAC+∠ACD=180°,
∴∠CAE+2x°+∠ACE+2y°=180°,
∴∠CAE+∠ACE=180°-(2x°+2y°),∠FAC+∠FCA=180°-(x°+y°)
∴∠AEC=180°-(∠CAE+∠ACE)
=180°-[180°-(2x°+2y°)]
=2x°+2y°
=2(x°+y°),
∠AFC=180°-(∠FAC+∠FCA)
=180°-[180°-(x°+y°)]
=x°+y°
∴∠AFC=
1 |
2 |
(2)如图2,连接AC,设∠EAF=x°,∠ECF=y°,∠EAB=3x°,∠ECD=3y°,
∵AB∥CD,
∴∠BAC+∠ACD=180°,
∴∠CAE+3x°+∠ACE+3y°=180°,
∴∠CAE+∠ACE=180°-(3x°+3y°),∠FAC+∠FCA=180°-(2x°+2y°)
∴∠AEC=180°-(∠CAE+∠ACE)
=180°-[180°-(3x°+3y°)]
=3x°+3y°
=3(x°+y°),
∠AFC=180°-(∠FAC+∠FCA)
=180°-[180°-(2x°+2y°)]
=2x°+2y°
=2(x°+y°),
∴∠AFC=
2 |
3 |
(3)若∠AFC=
1 |
n |
1 |
n |
n−1 |
n |